Given $ m \angle QPR = 7x + 63$, and $ m \angle RPS = 7x - 65$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
Solution: From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {7x + 63} + {7x - 65} = {180}$ Combine like terms: $ 14x - 2 = 180$ Add $2$ to both sides: $ 14x = 182$ Divide both sides by $14$ to find $x$ $ x = 13$ Substitute $13$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 7({13}) + 63$ Simplify: $ {m\angle QPR = 91 + 63}$ So ${m\angle QPR = 154}$.